FAQ/euclid - CBU statistics Wiki

You can upload content for the page named below. If you change the page name, you can also upload content for another page. If the page name is empty, we derive the page name from the file name.

File to load page content from
Page name
Comment
Type the missing letters from: He's no ded, he's jus resing hs eys

Revision 5 as of 2010-07-01 15:06:39

location: FAQ / euclid

# What is the formula for Euclidean distance ?

Euclidean distance measures the distance between two vectors of length t denoting t traits of various observations and is a specific example of Mahalanobis distance with an identity covariance matrix (ie uncorrelated traits).

ED = for vectors, observations with vectors $$x_text{i} = (x_text{1i}, ..., x_text_{ti}})text{T}$$ and $$x_text{j} = (x_text{1j}, ..., x_text_{tj})text{T}$$ equals $$\sqrt{(x_text{i} - x_text{j})^text{T}(x_text{i} - x_text{j})}$$

This can be written in long hand as $$\sqrt{(x_text{1i}-x_text{1j})text{2} + .. + (x_text{ti}-x_text{tj})text{2}}$$

The Euclidean distance is the distance on a graph between two points. This is easily seen in two dimensions since by Pythagoras's theorem the distance (hypotenuse) between two points (x11, x21) and (x12, x22) equals the square root of the squared difference in x and y co-ordinates = square root of (x11-x12)(x11-x12) + (x21-x22)(x22-x21). See [attachment:euclide.bmp here.]